I've never have run into an instance where I needed to do that with this material. The only thing I could suggest, provided you did in fact remove all of the oil, is that super glue comes in various qualities. For example, super glue, also known as CA glue, that you might find at a dollar store can be of a much lower quality than the CA glue you would find at a hobby store.
A good fairly high quality brand, that you can get at just about any major hardware store in the US is this.
The higher quality CA can be found at hobby stores like this.
But lets say that it's not the quality, but rather, CA simply doesn't adhere to frosted detail or frosted ultra detail, which there are some plastics that CA doesn't adhere to. In that case, you might try something like this from an industrial supplier.
Since FD and FUD are acrylics.